Differential Rings from Special Kähler Geometry

Abstract

We study triples of graded rings defined over the deformation spaces for certain one-parameter families of Calabi-Yau threefolds. These rings are analogues of the rings of modular forms, quasi-modular forms and almost-holomorphic modular forms. We also discuss some of their applications in solving the holomorphic anomaly equations.

reference added, typos corrected

References in corpus (4)

• On Rationally Parametrized Modular Equations
• Topological Strings and (Almost) Modular Forms
• Special Polynomial Rings, Quasi Modular Forms and Duality of Topological Strings
• Mahler Measure Variations, Eisenstein Series and Instanton Expansions

Cited by in corpus (7)

• LG/CY Correspondence for Elliptic Orbifold Curves via Modularity
• Ramanujan Identities and Quasi-Modularity in Gromov-Witten Theory
• Genus one GW invariants of quintic threefolds via MSP localization
• Mirror Symmetry for Plane Cubics Revisited
• GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities
• Algebraic structure of $t{t}^{\ast }$ equations for Calabi-Yau sigma models
• Lectures on BCOV holomorphic anomaly equations